Abstract
For a bare Coulomb potential energy -/r, it is shown that the total electron density ρ(r) for an arbitrary number of closed shells is given by ρ(r)=(2Z/) (r)dr where is the s-state contribution to ρ(r). This yields Kato’s theorem [∂ρ(r)/∂r=(-2Z/)ρ (r=0) as a limiting case. That ∂ρ/∂r is always negative follows, for all distances r. For the nth closed shell, with density (r), it is further shown that (r)=[(-/2Z)∂/∂r] , with the s-state radial wave function. This result can be used to construct an explicit differential equation for (r).
- Received 24 June 1985
DOI:https://doi.org/10.1103/PhysRevA.33.88
©1986 American Physical Society